Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Graph A represents the equation . Which other equations could Graph A represent?
Write three equations that Graph B could represent.
10.3
Activity
Standards Alignment
Building On
Addressing
8.F.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
For each situation, find the slope and intercepts of the graph. Then, describe the meaning of the slope and intercepts. Decide if the values you come up with are reasonable answers for the situation.
The printing company keeps an inventory of the number of cases of paper it has in stock.
The market value of a house is related to the size of the house.
Tyler teaches painting classes in which the amount of money he makes depends on the number of participants he has.
Mai tracks the amount of money in her no-interest savings account.
Priya earns coins for each new level she reaches on her game.
None
Standards Alignment
Building On
Addressing
8.EE.B
Understand the connections between proportional relationships, lines, and linear equations.
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.